Constructing Drainage Basin Models from DEM's–A Case Study of Chase
County, Kansas
John C. Davis1 and Günther Hausberger2
1Kansas
2Geo-
Geological Survey, 1930 Constant Ave., Lawrence, KS, USA 66047
und Umweltinformatik, Roseggerstraße 17, Leoben, Austria A-8700
Introduction
Contaminated surface waters have increasingly become a matter of concern in
the United States because of the health hazards they pose for both humans and
wildlife. Unfortunately, questions about the quality of surface water are difficult
to answer, in part because of a lack of sufficient information about the paths that
surface water follows as it flows across the ground and into streams. It is hard to
pinpoint possible sources of contamination in a timely manner because no
accurate inventory of stream drainage basins or stream catchment areas exists for
many areas, nor is there a mechanism for efficient extraction of such information.
The technology exists to create an interactive computer system which will
answer questions about surface waters and drainage basins. Software has been
written that will interactively query a file derived from a digital representation of
the topography of an area, yielding real-time answers to questions about the
properties of stream drainage basins and areas that drain into any designated
location. Such computer programs and digital files have been developed and
used in Austria (Hausberger and Hochreiter, 1995) and can be adapted for use in
the United States. Although for legal reasons the Austrian public has only
indirect access to their drainage basin data, we can imagine that in the United
States such files would be in the public domain and accessible interactively over
the Internet.
An initial digital database is derived from digital elevation models (DEMs) such
as the 1:24,000 scale models produced by the U.S. Geological Survey, and from
digital line graphs of hydrography at an equal or finer scale. The line graphs
usually are in the form of an ArcInfo vector layer or similar file. The DEM
topographic information typically must be corrected, rectified, and joined into
seamless, regional models of the land's surface. Stream courses defined by the
digital line graphs are "routed" into the surface to insure that all topographic
slopes lead into the drainage network. Then, a regional slope model is created
that permits boundaries to be determined between drainage basins of any size (a
practical lower limit defines drainage basins only 1 square kilometer or 247 acres
in extent). Once the boundaries of the basins have been defined, the program
calculates numerous statistics for any selected drainage basin. Most importantly,
if contaminants are identified at any location within the mapped area, either in a
stream or on the land surface, the program can interactively delineate all upslope
areas that might be a source of contaminants, and all downslope areas that might
be affected.
At present, the HUC-BOUND digital file of hydrologic unit boundaries is the
principal source of information on drainage basins over most of the United
States, and is available only at four discrete resolutions (Seaber, Kapinos and
Knapp, 1987). Watersheds smaller than 3,000 acres cannot be identified from
these data, and there is no interactive software to extract information from the
digital files. The U.S. Geological Survey has written WEASEL (Viger, Markstrom
and Leavesley, 2001), an interactive program for delineating drainage basins
from digital elevation models that has many characteristics in common with the
Austrian system, and a consortium based at the University of Texas–Austin is
working on similar methodologies (Mason and Maidment, 2000). However,
among other limitations, these software systems require that users purchase a
license for ArcInfo from ESRI in order to query their data. Drainage basin files
generated by the Austrian system are accessible through the ESRI product
ArcView Spatial Analyst, which costs a fraction of a full ArcInfo license.
The original experiments leading to the Austrian software began in 1990,
adapting grid-handling routines and algorithms in the SURFACE III contouring
package (Sampson, 1988). The drainage basin program became functional in 1994
and the first published results appeared the following year in Hausberger and
Hochreiter (1995). The software has been used to produce complete interactive
data bases of surface waters and drainage basins for the Austrian provinces of
Oberösterreich in 2000 and Niederösterreich early in 2001. Large parts of
Steiermark and Salzburg are included in these databases. The system is in
routine use by the provincial Bureau of Water and Hydrography
(Wasserwirtschaft und Hydrographie). Production of a similar data-base for the
province of Burganland is now underway, which also will include catchment
areas in the province of Steiermark. When completed, it will be possible to
interactively determine the drainage basin characteristics for all locations in
approximately half of the entire country of Austria.
To support a proposal to adapt the Austrian software system to American digital
elevation models, a pilot study has been done using data for Chase County,
Kansas (Fig. 1). The county is centered around 96°37'W, 38°15'N in the eastcentral part of the state. Chase County is in the Flint Hills physiographic
province, with elevations that range between approximately 1150 and 1640 ft
(350–500 m). The county has an area of 776 mi2 (2,010 km2) or 496,640 acres
(200,990 ha) and includes all of 9 U.S. Geological Survey 7.5 minute topographic
quadrangles and portions of 17 additional quadrangles. A level 2 digital
elevation model with a spatial resolution of 30 by 30 meters is available for each
quadrangle. Almost all of the streams in the county are tributaries of the
Cottonwood River, which in turn flows into the Neosho River, then into the
Arkansas River and eventually into the Mississippi River and the Gulf of Mexico.
Figure 1. (above) Index map of Chase County showing its location in Kansas.
(below) Shaded relief image of DEM of Chase County. Areas shown on the
following figures cover only the central third of the county.
Constructing a Digital Drainage Basin Model
Construction of a drainage basin model begins with a digital elevation model
(DEM), a regular array of values representing ground elevations. Typically, such
models consist of measurements of ground elevations at spacings of 30 meters
between rows and columns of the measurement points, although arrays having
greater resolutions (such as 10 meter DEMs) are becoming available. In the
United States, the U. S. Geological Survey provides DEMs for areas
corresponding to standard 7.5 minute topographic quadrangles. The DEMs are
by-products of the creation of quadrangle contour maps, or increasingly, as
special products generated by digitizing contours on pre-existing topographic
maps.
Usually, drainage basin models are wanted for areas that are much larger than
individual topographic quadrangles, so a series of DEMs must be joined together
to cover the area of interest. Inevitably, the quadrangle DEMs do not fit together
seamlessly, and they must be adjusted and corrected manually in order to create
a continuous representation of topography. Unless this is done, the completed
drainage basin model may contain artifacts along the joins.
It is possible to define drainage basins directly from DEMs (Marks, Dozier and
Frew, 1984; Jenson, 1991). However, the resulting drainage basins may not be
accurate, especially in areas of low surface gradients such as Kansas. The
drainage network produced from raw DEM data typically does not adequately
reproduce the known paths of stream channels, so queries about flow into
specified points along streams may return incorrect information. Figure 2 shows
the drainage basins generated for part of Chase Co., Kansas, using only rectified
and adjusted DEM's without additional information on stream locations.
Figure 2. Drainage basins for part of Chase Co., Kansas, generated directly from
30 m digital terrain model.
The 30-meter resolution of DEMs may not be adequate to define the drainage
system of an area, in part because the regular spacing of the DEM may result in
points along a stream course that alternately fall on the valley wall and in the
stream, producing a "string-of-pearls" effect of small closed depressions.
Fortunately, digitized vector representations of the hydrologic system usually
are available. These vector files represent the “blue” or hydrologic layer of
topographic maps and typically have greater resolution than the DEMs.
However, these vector files have characteristics that must be changed before they
can be used. Possible problems include imperceptible gaps in the digitized lines,
particularly where streams join or at the upper reaches where intermittent water
flow may be indicated by dashes. These gaps must be closed so the digitized
vectors form a completely linked stream network. Larger rivers may be
represented by double lines. To avoid logical problems in subsequent processing,
these double lines must be reduced to single center-lines. Lakes present similar
problems; the shores must be replaced by single vectors through the middle of
the lakes. Finally, some blue lines may form closed loops, or polygons. These
may result from errors in digitizing stream lines, the presence of islands in rivers
or lakes, the presence of canals or other artificial diversions of water from rivers,
or rarely, anastamosing or braided stream channels. These must be manually
resolved, preferably with advice from a hydrologist, so that the streams within
the area forms a continuous network without ambiguous pathways.
Once the vector layer representing the stream network has been rectified, it is
converted into a cellular approximation of the stream network that has the same
grid size and origin as the DEM. Cells that correspond to stream courses are
assigned a code value and all other cells remain blank. Each cell that represents a
stream in the resulting layer is assigned the elevation of the equivalent DEM cell.
The ArcInfo tool (line-to-grid) that rasterizes the vector stream network
generates a raster trace that is a stair-step function in which each cell joins an
adjacent cell along a face. The raster stream network can be regenerated
considering the flow directions in each cell, and some cells modified to run at 45°
directions; then, cells may be joined at their corners. This may improve the
rasterized approximation of the stream network, as shown in Figure 3.
Figure 3. Portion of stream channel network in part of Clark Co., Kansas, after
modification to allow 45° joins. Streams are color-coded by channel lengths.
A large constant value, such as 5000 meters, is added to each cell in the DEM, in
effect raising the ground surface by this amount. A logical operation is used to
combine the grid containing the elevated DEM surface with the grid representation of the stream network. This has the effect of "Einfräsen," or "routing in" the
stream network to assure that the stream channels are lower than any areas of
the ground surface and that all flow will eventually go into the stream channels.
This operation is approximately equivalent to the "burning in" process described
by Maidment (1996). Routing in river courses insures that the flow paths in
streams on the DEMs will be essentially identical to the actual river channels
shown on the blue layers of topographic maps. Without this step, there may be
significant differences, especially in areas where the bedrock is calcareous and
some drainage is underground.
Flow directions are calculated by comparing each cell of the modified DEM with
its neighboring cells and determining the relative differences in elevation
between them. This process will identify "sinks," cells with no flow directions
because they are lower than all surrounding cells and thus are local depressions.
In a DEM of an area in containing 50 million cells in Austria, about 120,000 sinks
were identified. It would not be surprising to find that up to 1% of the cells of a
modified DEM constitute sinks. The exact proportion of sinks depends upon
topography and the quality of the DEM. Sinks occur within the stream network
and also on slopes.
The ArcInfo FILL command is used to add to the values of each sink cell until
their elevations are equal to the values of the lowest neighboring cells. Then,
there will be a continuous slope from every high point in the DEM downhill to
the final outlet at the edge of the DEM. In other words, water will flow down
slope, into stream courses, and out of the model without ponding at any point.
However, it is possible that some areas may actually have true interior drainage.
In these circumstances, the closed depressions will fill up until they overflow into
the stream network. Then, every cell in the map area will have a flow direction.
The resulting array is the flow direction matrix. Figure 4 shows the flow
direction matrix for Chase Co. in which flow directions in eight classes of
direction have been indicated by color overlay.
Figure 4. DEM of Chase Co., Kansas, with flow direction by octant indicated by
color overlay for each cell.
A flow accumulation matrix is now generated by summing the number of cells
that feed into each cell; that is, the number of cells that are "upstream" from a cell.
If a cell has a flow accumulation number of zero, this means that the cell occupies
a topographic peak or is part of a watershed divide.
Drainage basins of specified size are defined by imposing a threshold on the
numbers of inflowing cells, which in effect specifies the maximum areas of
basins. The boundaries of the drainage basin are cells in which flow accumulation numbers are zero or very small values. The largest values of flow
accumulation occur in cells that represent stream channels. These values increase
abruptly where two streams join and the flow accumulations of both streams are
added together. Therefore, a drainage basin that is smaller than the threshold
value may abruptly exceed the specified threshold size at a junction of an
inflowing stream (Fig. 5). Stated in another way, stream junctions are identified
by comparing each cell in a stream network with the inflowing cells and
identifying those where the excess causes the drainage basin area (number of
cells) to exceed a threshold value. This is seen in greater detail in the enlarged
view of Figure 6.
Figure 6. Detailed view of drainage network in part of Chase Co., Kansas, colorcoded to indicate drainage areas (number of cells) feeding into streams.
A drainage basin is defined as the set of cells having flow directions that lead
into the cell immediately above the cell that exceeds the threshold value. Note
that any number of threshold values can be specified, leading to a progression of
smaller and smaller drainage basins (Figs. 7, 8). Presently used systems for
delineating drainage basins, such as HUC-BOUND and SWAT, are limited to a
few fixed levels of definition (U.S. Department of Agriculture, 1995).
Figure 5. Shaded DEM of Chase Co., Kansas, with stream channels color-coded
by drainage basin areas. Note abrupt changes in basin area classes at stream
junctions.
Figure 7. Shaded DEM overlain with drainage basin outlines color-coded to
indicate basin areas.
Figure 8. Drainage basin and sub-basin outlines, shown color-coded to indicate
basin size in square kilometers.
Using the Drainage Basin Model Interactively
After the drainage basins have been defined, it is relatively simple to generate a
variety of useful statistics which characterize the basins. Typical measures
include the areas of drainage basins; perimeters; minimum, maximum, and mean
elevations in basins; minimum, maximum, and mean slopes in basins; and
lengths of rivers in basins. It also is possible to identify each basin by a unique
point corresponding to the basin centroid. The centroid of the basin is
determined by finding the cell along the stream in which the inflow is equal to
one-half the area of the basin. Characteristics of the river in a basin also can be
generated easily, including the stream profile, the river gradient, and the
maximum, minimum, and mean elevation along the river. In addition to
summary statistics, is possible to produce and display distributions of all of these
characteristics for all basins in a mapped area (Fig. 9). The freeware Spatial
Analyst extension, "Watershed," from Ianko's GIS Page at the web site
(http://www.ian-ko.com/) was extensively modified to form the interactive
tool. The extension was rewritten to make it faster and more efficient and to
extend its capabilities.
Figure 9. Distribution of lengths of stream reaches, in meters. Similar
distributions and summary statistics for many properties can be created.
However, the most useful feature of the interactive drainage basin model is the
ability to identify all locations upstream from any point in a stream, not just at
stream junctions which define drainage basins. If a stream sample is collected in
a river and a chemical pollutant is detected in the water, all possible areas which
could contain the source of the contaminant can be immediately delineated on
the interactive model. Additional samples collected further upstream can be used
to refine the source; if an upstream sample is not contaminated, its drainage area
can be subtracted from the area defined by the contaminated sample.
The search for sources of contamination is not limited to stream courses. The set
of cells that feed into any cell, whether in a stream course or not, can be defined
in the interactive model. In effect, the drainage area into any location can be
delineated. This provides a powerful tool for designing an optimal search
strategy to find point-source contaminants. It can be equally effective for
delineating areas that may be non-point sources of contamination. Theoretically,
sources having areas as small as the DEM grid spacing could be defined, but a
source resolution of about 0.5 km2 (250 acres) is more practical for interactive
analysis. This is a significant improvement over current procedures which are
based on 1:100,000 digital grids and which cannot define areas smaller than the
smallest basin in a fixed hierarchy of sizes.
This procedure can be inverted, delineating the path of maximum descent from
any cell in a drainage basin. This is the track that will be taken by runoff that
exits the specified cell. If a point source such as a feedlot or leaking oil storage
tank is identified at a certain location, the movement of contaminants from the
source to the exit of the basin can be immediately determined. Thus, the
interactive software can be used to identify all potential sources for a
contaminant identified at any specific location, and to trace the route of possible
migration from the location to the outlet of the drainage basin.
Acknowledgements:
The authors would like to express their appreciation to Ms. Gina Ross and Dr.
David Collins of the Kansas Geological Survey for their help in conducting the
demonstration study of Chase County, Kansas, and for preparing the
illustrations that accompany this article.
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